gradians to radians | Exact Decimal + Formula

1 Gradian = 0.015708 Radian

One radian equals about 63.7 gradians (exactly 63.66197724 grad). Real-world use: surveying and some european engineering fields. This page expresses those values in radians, which is used for calculus, physics, and programming trigonometry functions. Enter any value above — the result updates instantly, and a 1–1000 reference table follows below.

About Gradian and Radian

Gradian (grad)

A gradian divides a right angle into 100 grads, so a full circle is 400 grads.

Where it's used: Surveying and some European engineering fields.

Radian (rad)

A radian is the angle subtended by an arc equal to the circle's radius; a full circle is 2π radians.

Where it's used: Calculus, physics, and programming trigonometry functions.

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Precision

Formula

rad = grad × 0.015707963

To convert Gradian to Radian, use the formula displayed above.

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Gradian to Radian: Quick Reference Table

Gradian	Radian (Decimal)	Fraction	Real-world equivalent
0.001 grad	0.000016 rad	-	fractional unit measurement
0.01 grad	0.000157 rad	-	fractional unit measurement
0.1 grad	0.001571 rad	-	fractional unit measurement
0.5 grad	0.007854 rad	-	fractional unit measurement
1 grad	0.015708 rad	-	fractional unit measurement
2 grad	0.031416 rad	-	fractional unit measurement
5 grad	0.07854 rad	-	fractional unit measurement
10 grad	0.15708 rad	-	fractional unit measurement
25 grad	0.392699 rad	-	fractional unit measurement
50 grad	0.785398 rad	-	fractional unit measurement
100 grad	1.570796 rad	-	standard single unit scale
250 grad	3.926991 rad	-	standard single unit scale
500 grad	7.853982 rad	-	standard single unit scale
1000 grad	15.707963 rad	-	multiple unit increments

grad to rad Formula and Examples

Direct Formula rad = grad × 0.015707963

Inverse Formula grad = rad × 63.661977

Mental Math Shortcut

Divide the value by roughly 63.7 to quickly estimate the converted result.

Common Gradian to Radian Calculations

5 grad = 0.07854 rad
10 grad = 0.15708 rad
50 grad = 0.785398 rad
100 grad = 1.570796 rad
500 grad = 7.853982 rad

Precision & Practical Use

For example, 10 grad = 0.15708 rad — roughly fractional unit measurement.

Results are computed to up to 9 decimal places. Round to the precision of your measuring instrument — for most angle applications, 2–3 significant figures are plenty.

How to Convert Gradian to Radian

How many radians are in one gradian?

One Gradian (grad) equals 0.015708 Radian (rad). To convert gradians to radians, multiply the gradian value by 0.015708.

How do I convert Gradian to Radian?

Multiply your gradian value by 0.015708 to get the result in Radian: rad = grad × 0.015708. For example, 5 grad = 0.07854 rad.

What is the formula for converting grad to rad?

The conversion formula is rad = grad × 0.015708. Use the calculator above for any value, and see the reference table below for common inputs from 0.001 to 1000.

Is there a quick mental estimate for grad to rad?